Slab analysis of roll bonding of silver clad phosphor bronze sheets

Abstract

A numerical analysis program, based on slab analysis, was developed to calculate the stresses and strains that occur in the component layers of a composite sheet in the roll bite during the fabrication of clad metal (e.g. silver clad phosphor bronze) by roll bonding. Results calculated using the perfect plastic and strain hardening models were compared with experimental results: the results obtained using the strain hardening model were found to be in better agreement with values of rolling force and thickness of component layers measured after roll bonding. The program requires input data such as roll radius, initial thickness of the specimen, initial cladding thickness fraction, reduction ratio, coefficients offriction between rolls and material and between component layers, and front and back tensions. The coefficients offriction were evaluated indirectly by comparison of the measured rolling force with that calculated using slab analysis. Measured coefficients of friction varied with reduction ratio and initial thickness, but were independent of rolling speed.MST/1334 List of symbolsh thickness of monolithic or composite sheet after rolling, mm hA, hB thickness of soft and hard layers, respectively, mm H initial thickness of monolithic or composite sheet, mm HA, HB initial thickness of soft and hard layers, respectively, mm k A , k B shear yield stress of soft and hard layers, respectively, MN m-2 k A mean shear yield stress of Ag, MN m -2 P vertical pressure, MN m -2 PA, PB rolling pressure on soft and hard layers, respectively, MN m-2 PAB pressure on soft/hard layer interface, MN m-2Pc, Pe calculated and experimental rolling force, respectively q soft/hard layer thickness ratio r reduction ratio RA, RB radius of roll in contact with soft and hard layers, respectively, mm v rolling speed, m s -1

Cold roll bonding of multi-layered bi-metal laminate composites

“…In zone two, both of the materials yield. The slab method of analysis was also used in another study wherein the numerical results obtained for silver clad phosphor bronze were compared with actual experimental results [22]. Further studies involved analysis of rolling of two layers or three layers bi-metal sheets without using a numerical method [23,24].…”

“…With the objective of predicting the rolling force and torque, a few models have been devised for roll bonding of two or three layer systems [21][22][23][24][25][26][27][28]. These deal primarily with the cladding of metals.…”

Analysis of asymmetrical cold and hot bond rolling of unbounded clad sheet under constant shear friction

“…Lee and Lee [2] performed cold roll bonding for silver and phosphor bronze sheets under the same roll radii, and analysis assuming Coulomb friction together with the Runge-Kutta numerical method to obtain the rolling pressure and thickness ratio of clad sheet at the exit. The CPU time required is too great to obtain more detailed information.…”

“…Studies concerning clad sheet rolling can be divided into experimental studies [1,2] and theoretical studies [3][4][5][6][7][8][9][10][11][12][13]. Lee and Lee [2] performed cold roll bonding for silver and phosphor bronze sheets under the same roll radii, and analysis assuming Coulomb friction together with the Runge-Kutta numerical method to obtain the rolling pressure and thickness ratio of clad sheet at the exit.…”

Slab Analysis of Asymmetrical Rolling of Bonded Two-layer Sheets

“…Lee and Lee 1) studied cold roll bonding of silver and phosphor bronze sheets by the slab method to numerically calculate the rolling pressure. Tzou et al 2) utilized the slab method to analyze the cold and hot bond rolling of double-layer clad sheets.…”